Representation of contractively complemented Hilbertian operator spaces and the Fock space

Abstract

The operator spaces \(H_n^k\) \(1\le k\le n\), generalizing the row and column Hilbert spaces, and arising in the authors' previous study of contractively complemented subspaces of \(C^*\)-algebras, are shown to be homogeneous and completely isometric to a space of creation operators on a subspace of the anti-symmetric Fock space. The completely bounded Banach-Mazur distance from \(H_n^k\) to row or column space is explicitly calculated.